Constraint Definition and 184 Threads

PROBLEM STATEMENT: Determine if f(x,y) = x^2+y^2 has a maximum and a minimum when we have the constraint 2x^3+3x^{2}y+3xy^{2}+2y^3=1. (1) ATTEMPT TO SOLUTION: A standard way of solving these kinds of problems is by using the Lagrangian multiplier-method. It consists of comparing the gradient of...

Homework Statement So I've worked this problem for awhile. Its a several page of math problem with optimization, legrangians, cramers rule, etc to get to this point. All I need to do now is by hand solve this equation for x and y with the constraint. Homework Equations -0.03x^2 + 40x...

Homework Statement The Attempt at a Solution Can anyone explain why there is a force constraint in the z direction. The pin force only affects the x and y... Also shouldn't there be a moment in the z since the pin prevents the block from rotating cw and ccw in the xy plane?

Are fictitious forces and constraint forces the same thing?

Hello I need some help with formulating the constraint force for a sliding and rotating box. The scenario is: A box is sliding down a slanted table. The center of gravity has passed the edge of the table so the box receives a counter force and torque. I am solving the forces and moments...

Hi all, I was having a bit difficulty understanding the term scleronomic constraint. From what I have read, it is a type of holonomic system(which means there is time dependence). However, the difference between the two types(scleronomic and rheonomic), is that although scleronomic...

In this paper called "Stepping out of Homogeneity in Loop quantum Cosmology" - http://arxiv.org/pdf/0805.4585.pdf. On page 4 they say "where the sum is over the couples of distinct faces at each tetrahedron, U_{ff'} = U_f U_{f_1} U_{f_2} \dots U^{-1}_{f'} where l_{ff'} = \{ f , f_1; f_2; \dots...

Suppose you are trying the solve the equation of motion of say a particle constrained to move on a surface f(x\vec{},t)=0. The equation of motion is: mx\ddot{} = F\vec{} + N\vec{}, where F is an known external force and N is the unknown constraint force. Now, when you assume that N always...

Homework Statement Consider f(x,y) = \frac{1}{x} - \frac{1}{y} You need to maximize f(x,y) given the constraint: x + y = 11 Homework Equations I have never solved a problem like this before. In fact I made up a problem a few minutes ago. The Attempt at a Solution I...

Hello, I need to find (if there are) minimum and maximum values of the following function: z=\frac{1}{x}+\frac{1}{y} subject to constraint: \frac{1}{{x}^{2}}+\frac{1}{{y}^{2}}=\frac{1}{{a}^{2}} a\neq 0 I think there are no extrema, but I do not know how to show it.

The problem is in the attached document. Thanks for any suggestions! Lennart

Homework Statement What is the acceleration of the 2. kg block in the figure across the frictionless table? Homework Equations F=ma The Attempt at a Solution g = 9.8ms^2

Homework Statement What is the maximum possible volume of a rectangular box inscribed in a hemisphere of radius R? Assume that one face of the box lies in the planar base of the hemisphere. NOTE: For this problem, we're not allowed to use Lagrange multipliers, since we technically haven't...

Homework Statement I want to be able to plot a trajectory wrt time of a ball that rolls without slip on a curved surface. Known variables: -radius/mass/moment of inertia of the ball. -formula for the curvature of the path (quadratic) -formula relating path length and corresponding height...

Homework Statement An object is constrained by a cord to move in a circular path of radius 0.5m on a horizontal frictionless surface. The cord will break if tension exceeds 16N. The maximum kinetic energy the object can have is:Homework Equations KE=1/2mv^2 U=mgh The Attempt at a Solution...

Homework Statement Find the maximum and minimum values of f(x,y) = 2x^2+4y^2 - 4xy -4x on the circle defined by x^2+y^2 = 16. Homework Equations Lagrange's method, where f_x = lambda*g_x, f_y= lambda*g_y (where f is the given function and g(x,y) is the circle on which we are looking...

There's a new paper dealing with constraint algebra and Gupta-Bleuler quantization in LQG and SF models. http://arxiv.org/abs/1012.1738 Complex Ashtekar variables and reality conditions for Holst's action Authors: Wolfgang Wieland (Submitted on 8 Dec 2010) Abstract: From the Holst action...

Homework Statement Find : a) acceleration of 1 kg, 2kg and 3 kg blocks and b) tensions T1 and T2 Note: In the figure, 1, 2 and 3 represent the masses of respective blocks in Kg. T1 and T2 represent tension in strings Homework Equations Newton's laws and constraint equations...

Hi, What exactly is the condition for a constraint to be ideal? Let's call the net force of constraint on particle i \bar{N_i}. Is the condition \sum_i\bar{N_i}\cdot\delta\bar{r_i}=0? Or is it \bar{N_i}\cdot\delta\bar{r_i}=0 for each i? (from which the first follows immediately) From the...

while solving Lagrangian of a system to derive equations of motion in presence of a constraint, I have finally landed down to a system of 3 coupled ODEs , where i have two variables(x and y) and 1 Lagrange multiplier. ODEs are of order 4,3 and 1 respectively. L1(x,y)=lambda L2(x,y)=0...

For my economics/game theory thesis I need to optimize a function subject to an inequality constraint. maximize f(x1, x2) = 1/(x1+x2+y1+y2-w) subject to g(x1, x2) = x1+x2+y1+y2 < w This isn't particularly important, but the x and y variables are quantity of production by a firm. The objective...

I am trying to ultimately find the projector onto a convex set defined in a non-explicit way, for a seismic processing application. The signals in question are members of some Hilbert Space H and the set membership requires that they must correlate with each other above some scalar \rho, given...

How do constraint equations in mechanics work? Hi, friends! I'm having some trouble understanding the constraint equations:- (1) How do they relate the length of the string to the position of the block attached to it? The position of the block must be a vector and it must be differentiated...

Let's say we have a circuit composed of simple linear circuit elements (resistors, inductors and capacitors). Now we calculate the Thevenin equivalent circuit for some load within this circuit, and we determine the Thevenin impedance, Z_t. My question is this: Is it generally the case that...

I am currently solving a problem (similar to optimal control theory) involving optimization of an integral with mixed and pure constraints. eg: \int F(x,u,t) dt subject to x(t)\geq0 , u(t)\geq0. The problem can be solved by Pontryagin minimum principle by introducing the Hamiltonian function...

Hello all, I don't have much experience with ODEs. I have a simple system, which I believe is first order linear, similar to the following: dA/dt = 2A + 3B - C dB/dt = A + 2B - C dC/dt = -2A + 5B - 2C Now I would like to include the constraint that A + B + C = 1. How do I do this...

Homework Statement A particle of mass m moves under a uniform gravitational field along a rod which moves in a vertical plane with a constant angular velocity \vec \Omega. Write down the motion equations of the particle and calculate the constraint force. Is the energy conserved...

About the Analytical Physics constraint writing... I have added a photo about my problem. My problem is why did we write while calculating constraint values as d/2. you will see on the picture what I am saying, I cannot see the reason of writing d/2

Hey guys, What exactly does a nonholonomic constraint tell about a system. For instance I am working on a goldstein problem and it has raised the importance of interpreting what a constraint really does. I understand what a holonomic constraint is and what it tells me-for one the motion is...

Homework Statement I am doing some review and I though that I had this down pat, but I am getting confused a little. I am looking at the Wikipedia on Mesh Analysis. I do not understand the last equation of each section. How are they getting the signs of the currents? In the top image...

Hi, I hope this is going in the proper place, its essentially maximizing a matrix so here goes: Given the independant variables a, b, c, d, and e, and the system [ 1 1 0 5 1 | A ] [ 0 3 0 1 1 | B ] [ 4 1 1 0 1 | C ] [ 1 0 3 1 0 | D ] I want to find the a, b, c, d, and e that will...

Homework Statement A uniform rod of length l rests on a horizontal floor and leans against a vertical wall, making an angle \theta with the floor. It is initially held at rest. At t = 0, the rod is released and falls, sliding on the floor and the wall with no friction. The only forces acting on...

I have already read one thread on Lagrange's method of variation of parameters and it was very useful, but I am still confused about the use of the constraint. If the solution to the homogeneous second order equation contains two functions, with arbitrary constants: y= Ay1 + By2...

Homework Statement Please see the attached file for the problem and figure. Homework Equations The Attempt at a Solution This is what I have so far: The position vector of the block, pblock= xblock wx+ yblock wy pblock dot omegaz=0 holonomic constraint equation (dot product) n=3N-M...

Homework Statement Let h be an observed value at a given time t t = 5, 10, 20, 30, 40, 50 h = 0.72, 0.49, 0.30, 0.20, 0.16, 0.12 Let h* be a modeled estimate of hHomework Equations h* = [ Q / 4*Pi*T*t ] * e [ - (d^2)*S / 4*T*t ] where the known constants are Pi, Q (= 50), and d (= 60)...

Homework Statement Hello. I need help with a problem that deals with the acceleration constraint of a system (URL below is to an image of the system): http://s3.amazonaws.com/answer-board-image/e8ee7c74-664f-4220-a394-fc2b3d5bc269.jpeg The questions asked in the problem are as...

Dear all, Consider the system given by : http://www.freeimagehosting.net/image.php?53f7eed9ce.jpg where we are trying to solve for s and gamma using Newton's method. It turns out to be a simple implementation. Now, what if we need to impose an inequality constraint on the solution s : one...

when a particle is constraint to move on a circle, what are the constraint forces

Minimizing a function with a minimum constraint... Homework Statement A firm would like to produce q units of output at the lowest cost. It's cost structure is rk + wL. Minimize this function with respect to the constraint: min {sk, L/S} = q K = represents capital l = represents labor...

Homework Statement z = cr^2 Homework Equations The Attempt at a Solution I have a pretty simple question. What is the second derivative of the z equation. I know that z' = 2crr'. Am I correct to say that z'' = 2cr'^2 or is it something else? Hopefully my question...

Homework Statement Let f(x,y,z)=0 and r=r(x,y,z) be another constraint. show that if r is held constant then (\partial x/\partial y)_r *(\partial y/\partial z)_r *(\partial z/\partial x)_r = 1 hint: consider dr and use the fact: (\partial x/\partial y)_z *(\partial y/\partial...

Homework Statement Could you write the constraint equation for this system by using the only coordinates given in the question. (x1 and y1 for the center of mass m and X is the x coordinate of wedge) http://img602.imageshack.us/img602/34/imagea.jpg...

Homework Statement A simple pendulum has a mass M attached at the end of a massless rod of length L. Find the force of constraint the rod exerts on the bob. Homework Equations The Attempt at a Solution It seems easy enough that the mass is constrained by the tension the rod...

I assume you want to equate theta and phi somehow that would express the "natural" motion of the system. In this case, you could equate the length of the inside of the cylinder with some multiple of the circumference of the sphere as it travels along there. You could also equate the arc length...

A field K is called algebraically closed field if any no-zero polynomial has at least one root in K. Given finite field F_q, q=p^m, p is a prime and m is non-negative integer. A famous property of finite field is any element in F_q satisfies: x^q=x. Then I have such an assumption...

http://img221.imageshack.us/img221/3754/capturetp.png Just a simple question. I can see that for this to work I need: Trot = 1/5 ma2(thetaDOT + phiDOT)2 Just can't work out what phi has to do with rotational kinetic energy. I would have thought it would need to be simply the same thing but...

Homework Statement Solve the following problems using Lagrange multipliers (a) Minimise J (x; y) = x^2 + y^2 subject to C (x; y) = 4x^2 + 3y^2 = 12: Homework Equations The Attempt at a Solution i got h(x,y)=x^2+y^2+\lambda(4x^2+3y^2-12) dh/dx=2x+8x\lambda=0 dh/dy=2y+6y\lambda=0 then i got...

Homework Statement A particle of mass M is constrained to move on a ring of radius r which rotates about a vertical axis (Y) passing through the center at a constant angular speed (omega). I am to find the constraint equation(s) for this system. The origin of the system is at the...

Thanks so much guys

Can questions like the one given in the following pic be solved by taking the reference frame answhere in the middle of the string and not on the fixed pulley?(http://cnx.org/content/m14731/latest/pq8.gif) A somewhat similar method has been given in http://cnx.org/content/m14783/latest/"...